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Square numbers n for which sigma(n) - d(n) is also a perfect square.
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%I #43 Apr 12 2013 13:13:21

%S 1,4,1276900,7236100,9449476,69529779225,273137935876,275693254225,

%T 1011814692100,1590221881600,3007619594001,5382738725329,

%U 6343774129225,10830009646404,43037339281225,49597341481444,161977776248401,492275260674729,623724701219361

%N Square numbers n for which sigma(n) - d(n) is also a perfect square.

%e 4 is in the list since 4 = 2^2 and sigma(4)-d(4) = 4 = 2^2. Also 9449476 = 3074^2 and sigma(9449476)-d(9449476) = 17455684 = 4178^2.

%t Sqd[n_] := Sqrt[DivisorSigma[1, n] - DivisorSigma[0, n]]; t = {}; Do[p = n^2; If[IntegerQ[Sqd[p]], AppendTo[t, p]], {n, 7000000}]; t

%Y Cf. A221856.

%K nonn

%O 1,2

%A _Jayanta Basu_, Apr 11 2013

%E a(16)-a(19) from _Donovan Johnson_, Apr 11 2013